Gas Cost Estimator: estimation of impact of arguments on gas costs
In this script we conduct the estimation for the
measure_arguments approach. It is to verify and detect
arguments cost for opcodes execution.
Below are the parameters used for this report.
EVM client ENV=geth.
The file with programs PROGRAMS=pg_arguments_arithmetic.csv.
The file with measurement results RESULTS=results_arguments_arithmetic_geth.csv.
The optional comma separated list of estimated costs obtained in the marginal procedure MARGINAL_ESTIMATED_COST-.
The optional file to output estimated costs and results OUTPUT_ESTIMATED_COST-.
if ( !removed_outliers) {
boxplot(measure_total_time_ns ~ opcode, data=measurements, las=2, outline=TRUE, log='y', main=paste(env, 'all'))
}if (removed_outliers) {
par(mfrow=c(2, 1))
# before
boxplot(measure_total_time_ns ~ opcode, data=measurements, las=2, outline=TRUE, log='y', main=paste(env, 'all'))
measurements = remove_outliers(measurements, 'measure_total_time_ns')
# after
boxplot(measure_total_time_ns ~ opcode, data=measurements, las=2, outline=TRUE, log='y', main=paste(env, 'no_outliers'))
}
Detailed view
This is massive and detailed overview on the impact of arguments.
Because of the number of charts, only op count = 30 is
eligible. Feel free to change it, but that should not be anyhow more
informative. The visualizations do not guarantee that all dependencies
are clearly seen. Especially for binary and ternary opcodes where
impacts of arg0, arg1 and arg2 are mixed. But if a dependency is
graphically noticeable that you should expect also statistical
dependency.
for(i in 1:nrow(opcode_arity_df)) {
opcode_arity <- opcode_arity_df[i,]
opcode <- opcode_arity[["opcode"]]
# skip opcodes without measurements
if(length(which(measurements$opcode == opcode & measurements$op_count == 30)) == 0) {
next
}
arity <- opcode_arity[["arity"]]
if (arity >= 1) {
plot(measure_total_time_ns ~ arg0, data=measurements[which(measurements$opcode == opcode & measurements$op_count == 30), ], pch=5, col='blue')
title(main = paste(env, opcode, 'arg0', 'opcount 30'))
}
if (arity >= 2) {
plot(measure_total_time_ns ~ arg1, data=measurements[which(measurements$opcode == opcode & measurements$op_count == 30), ], pch=5, col='blue')
title(main = paste(env, opcode, 'arg1', 'opcount 30'))
}
if (arity >= 3) {
plot(measure_total_time_ns ~ arg2, data=measurements[which(measurements$opcode == opcode & measurements$op_count == 30), ], pch=5, col='blue')
title(main = paste(env, opcode, 'arg2', 'opcount 30'))
}
}
Models
This is the so-called “first-pass” at the estimation procedure, where
we estimated all possible argument impact variables for all OPCODEs. We
gather all the results in the first_pass table, inspect
this to see where the arguments turned out to be significantly impacting
the computation cost.
The argument is considered impacting on the gas cost of opcode execution if its coefficient in the regression model
- is noticeable comparing to the marginal cost (at least 0.01 %),
- has high correlation (Pr(>|t|)=Pr(>|Estimate/Std. Error|)<0.001).
Moreover, these opcodes are considered having impacting arguments by default as they are explicitly included in the current gas cost calculation.
- EXP, arg1
- KECCAK256, arg1
- CALLDATACOPY, arg2
- CODECOPY, arg2
- EXTCODECOPY, arg2
- RETURNDATACOPY, arg2
- MCOPY, arg2
- LOG0, arg1
- LOG1, arg1
- LOG2, arg1
- LOG3, arg1
- LOG4, arg1
- CREATE, arg2
- RETURN, arg1
- CREATE2, arg2
- REVERT, arg1
Below is the listing of arguments impact.
if (details) {
args_estimates
} else {
args_estimates[which(args_estimates$has_impacting), ]
}## opcode arg ns_raw ns_p has_impacting
## 1 ADD 0 2.29123494 8.777741e-03 FALSE
## 2 ADD 1 0.90691340 2.874219e-01 FALSE
## 3 ADDMOD 0 1.10412753 2.250864e-01 FALSE
## 4 ADDMOD 1 1.30702925 1.685927e-01 FALSE
## 5 ADDMOD 2 -0.59812483 5.835785e-01 FALSE
## 6 AND 0 -0.77395381 3.495778e-01 FALSE
## 7 AND 1 -0.64204584 4.753191e-01 FALSE
## 8 BYTE 0 -0.39576077 6.595761e-01 FALSE
## 9 BYTE 1 0.59245938 5.017880e-01 FALSE
## 10 DIV 0 1.14360519 3.516143e-01 FALSE
## 11 DIV 1 -0.31547091 7.874282e-01 FALSE
## 12 EQ 0 -2.15854080 1.164984e-02 FALSE
## 13 EQ 1 -0.46463851 6.041499e-01 FALSE
## 14 EXP 0 0.33560857 5.821580e-01 FALSE
## 15 EXP 1 30.84189760 5.897099e-225 TRUE
## 16 GT 0 -0.51009221 5.789402e-01 FALSE
## 17 GT 1 0.40077936 6.523409e-01 FALSE
## 18 ISZERO 0 -1.41542616 1.140299e-01 FALSE
## 19 KECCAK256 0 0.01141304 3.231326e-01 FALSE
## 20 KECCAK256 1 1.58341819 0.000000e+00 TRUE
## 21 LT 0 -0.47833838 5.896978e-01 FALSE
## 22 LT 1 0.56664144 5.345833e-01 FALSE
## 23 MOD 0 0.20448844 8.677863e-01 FALSE
## 24 MOD 1 0.88967145 4.666156e-01 FALSE
## 25 MUL 0 0.05054622 9.542560e-01 FALSE
## 26 MUL 1 0.81113273 3.585138e-01 FALSE
## 27 MULMOD 0 -0.02743146 9.751914e-01 FALSE
## 28 MULMOD 1 -0.07435254 9.326493e-01 FALSE
## 29 MULMOD 2 0.25813993 7.818149e-01 FALSE
## 30 NOT 0 0.25668277 7.679307e-01 FALSE
## 31 OR 0 0.53545283 5.335712e-01 FALSE
## 32 OR 1 -1.87314092 2.944656e-02 FALSE
## 33 SAR 0 1.35188625 1.330102e-01 FALSE
## 34 SAR 1 0.69118091 4.364115e-01 FALSE
## 35 SDIV 0 0.22359576 8.606565e-01 FALSE
## 36 SDIV 1 0.98912846 4.179878e-01 FALSE
## 37 SGT 0 0.57945060 5.355509e-01 FALSE
## 38 SGT 1 0.84826571 3.162259e-01 FALSE
## 39 SHL 0 -0.29011344 7.300892e-01 FALSE
## 40 SHL 1 0.17484256 8.414497e-01 FALSE
## 41 SHR 0 0.91181945 2.916879e-01 FALSE
## 42 SHR 1 -1.91350689 2.454875e-02 FALSE
## 43 SIGNEXTEND 0 0.33157733 6.932240e-01 FALSE
## 44 SIGNEXTEND 1 -0.70005733 4.195110e-01 FALSE
## 45 SLT 0 0.17198676 8.453711e-01 FALSE
## 46 SLT 1 -0.15901532 8.515104e-01 FALSE
## 47 SMOD 0 -0.76751431 5.204208e-01 FALSE
## 48 SMOD 1 -0.27172729 8.200405e-01 FALSE
## 49 SUB 0 -0.49804663 5.754823e-01 FALSE
## 50 SUB 1 -0.38779647 6.612229e-01 FALSE
## 51 XOR 0 0.03085968 9.702871e-01 FALSE
## 52 XOR 1 -0.83092885 3.211598e-01 FALSEThe blue graph is the measurements, the red line is the estimated arguments cost shifted by the estimated constant cost of the programs execution. The default opcodes count is 30.
proceed_with_opcodes <- first_pass[which(first_pass$has_impacting), "opcode"]
for(opcode in proceed_with_opcodes) {
if (nrow(measurements[which(measurements$opcode == opcode & measurements$op_count == 30), ]) == 0) {
stop(paste("measurements for ", opcode, "are invalid, there are no measurements for op_count==30"))
}
opcode_estimates <- first_pass[which(first_pass$opcode == opcode),]
if (opcode_estimates[["has_impacting_arg0"]]) {
slope = opcode_estimates[["arg0_ns_raw"]] * 30
intercept = opcode_estimates[["intercept"]] + opcode_estimates[["estimate_marginal_ns"]] * 30
xmax = max(measurements[which(measurements$opcode == opcode & measurements$op_count == 30), "arg0"])
ymin = min(measurements[which(measurements$opcode == opcode & measurements$op_count == 30), "measure_total_time_ns"], intercept, intercept + slope * xmax)
ymax = max(measurements[which(measurements$opcode == opcode & measurements$op_count == 30), "measure_total_time_ns"], intercept, intercept + slope * xmax)
plot(measure_total_time_ns ~ arg0, data=measurements[which(measurements$opcode == opcode & measurements$op_count == 30), ], pch=5, col='blue', ylim=c(ymin*0.95, ymax*1.05))
title(main = paste(env, opcode, 'arg0', 'opcount 30'))
abline(a=intercept, b=slope, col="red")
}
if (opcode_estimates[["has_impacting_arg1"]]) {
slope = opcode_estimates[["arg1_ns_raw"]] * 30
intercept = opcode_estimates[["intercept"]] + opcode_estimates[["estimate_marginal_ns"]] * 30
xmax = max(measurements[which(measurements$opcode == opcode & measurements$op_count == 30), "arg1"])
ymin = min(measurements[which(measurements$opcode == opcode & measurements$op_count == 30), "measure_total_time_ns"], intercept, intercept + slope * xmax)
ymax = max(measurements[which(measurements$opcode == opcode & measurements$op_count == 30), "measure_total_time_ns"], intercept, intercept + slope * xmax)
plot(measure_total_time_ns ~ arg1, data=measurements[which(measurements$opcode == opcode & measurements$op_count == 30), ], pch=5, col='blue', ylim=c(ymin*0.95, ymax*1.05))
title(main = paste(env, opcode, 'arg1', 'opcount 30'))
abline(a=intercept, b=slope, col="red")
}
if (opcode_estimates[["has_impacting_arg2"]]) {
slope = opcode_estimates[["arg2_ns_raw"]] * 30
intercept = opcode_estimates[["intercept"]] + opcode_estimates[["estimate_marginal_ns"]] * 30
xmax = max(measurements[which(measurements$opcode == opcode & measurements$op_count == 30), "arg2"])
ymin = min(measurements[which(measurements$opcode == opcode & measurements$op_count == 30), "measure_total_time_ns"], intercept, intercept + slope * xmax)
ymax = max(measurements[which(measurements$opcode == opcode & measurements$op_count == 30), "measure_total_time_ns"], intercept, intercept + slope * xmax)
plot(measure_total_time_ns ~ arg2, data=measurements[which(measurements$opcode == opcode & measurements$op_count == 30), ], pch=5, col='blue', ylim=c(ymin*0.95, ymax*1.05))
title(main = paste(env, opcode, 'arg2', 'opcount 30'))
abline(a=intercept, b=slope, col="red")
}
}
Expensive and trivial modes
In some cases an execution of opcode is trivial. For instance DIV x, y for x < y fives 0 without further work. For selected opcodes we investigate the trivial mode and so the called expensive mode when typical algorithm needs to be run fully.
first_pass[which(!is.na(first_pass$expensive_ns_raw)), c("opcode", "estimate_marginal_ns", "estimate_marginal_ns_p", "expensive_ns_raw", "expensive_ns_p")]## opcode estimate_marginal_ns estimate_marginal_ns_p expensive_ns_raw
## 2 ADDMOD 8.049708 0.7959371 -33.269516
## 5 DIV -11.378359 0.6467815 -5.666009
## 12 MOD -23.148542 0.3628147 23.198470
## 14 MULMOD 39.281711 0.1748634 -15.479091
## 18 SDIV -8.774008 0.7196046 8.607449
## 24 SMOD 14.347613 0.5518920 -4.558836
## expensive_ns_p
## 2 0.1955791
## 5 0.8362751
## 12 0.4066609
## 14 0.5642700
## 18 0.7577850
## 24 0.8657557Heat maps help to visualize dependency between two arguments, in particular division into trivial and expensive modes. Other strong or weak dependencies can be also detected.
for(opcode in proceed_with_opcodes) {
working_args <- args_estimates[which(args_estimates$opcode == opcode), "arg"]
if (length(working_args) == 1) {
plot_args_dependency_1(measurements, opcode, working_args[[1]])
} else if (length(working_args) == 2) {
plot_args_dependency_2(measurements, opcode, working_args)
}
}
Verification against marginal estimations
In this section we compare opcodes cost obtained in the arguments course with previous estimations obtained in the marginal procedure.
No marginal estimated cost files given.
if (params$output_estimated_cost != "") {
write.csv(first_pass, params$output_estimated_cost, quote=FALSE, row.names=FALSE)
}